where \(\mathbf {m}(\mathbf {r}) = \mathbf {M}(\mathbf {r})/M_{\mathrm {s}}\)  denotes the unit magnetization vector with \(M_{\mathrm {s}}\)  the saturation magnetization, \(\mathbf {H}_0 \parallel \mathbf {e}_z\)  is the (constant) applied magnetic field, \(\mathbf {H}_{\mathrm {D}}(\mathbf {r})\)  is the magnetostatic self-interaction field, \(K_1\)  is the first-order cubic anisotropy constant, \(A\)  is the exchange-stiffness constant, \(\mu _0 = 4\pi \times 10^{-7} \, \mathrm {Tm/A}\) , and the integrals are taken over the volume of the sample. In the simulations, we used the following material parameters for iron (Fe): saturation magnetization \(M_{\mathrm {s}} = 1700 \, \mathrm {kA/m}\) , exchange-stiffness constant \(A = 1.0 \times 10^{-11} \, \mathrm {J/m}\) , and a first-order cubic anisotropy constant of \(K_1 = 47 \, \mathrm {kJ/m^3}\) . These values result in a critical single-domain diameter of \(D_{\mathrm {cr}}^{\mathrm {sd}} \sim 72 \sqrt{A K_1}/(\mu _0 M_{\mathrm {s}}^2) = 13.6\)  nm [1]}.
<FIGURE>